ABSTRACT A simple method to amplify the micro displacements produced by magnetostrictive effect, giant magnetostrictive, converse piezoelectric and photo strictive effect, respectively, is reported. The device consists mainly of two material rods with different coefficients of strains vs intensity of external fields, which are rigidly jointed, so that the displacements created by different rods can be added directly. In contrast with all other methods reported so far, which are all based on the principle of lever, this approach holds some unique advantages that can be applied to respond to the electromagnetic fields with high frequency because there is no friction caused by the relative motion between levers and furthermore, an ideal and smooth amplification of micro displacement can be obtained with ease in principle.

1. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
DOI : 10.5121/ijics.2016.6301 1
A SIMPLE METHOD TO AMPLIFY MICRO
DISPLACEMENT
Yizong He and Jian-Ping Wang
Department of Electrical and Computer Engineering, University of Minnesota,
Minneapolis, MN 55455, USA
ABSTRACT
A simple method to amplify the micro displacements produced by magnetostrictive effect, giant
magnetostrictive, converse piezoelectric and photo strictive effect, respectively, is reported. The device
consists mainly of two material rods with different coefficients of strains vs intensity of external fields,
which are rigidly jointed, so that the displacements created by different rods can be added directly. In
contrast with all other methods reported so far, which are all based on the principle of lever, this approach
holds some unique advantages that can be applied to respond to the electromagnetic fields with high
frequency because there is no friction caused by the relative motion between levers and furthermore, an
ideal and smooth amplification of micro displacement can be obtained with ease in principle.
KEYWORDS
Amplification of micro displacement, Wagneto strictive effect, Giant magneto strictive effect, Converse
piezoelectric effect, Photo strictive effect
1. INTRODUCTION
In order to gain a smooth puller for Czochralski technique of crystal growth, a novel puller was
proposed in 1999, which pulling process of single crystals is not carried out by traditional gear
motors, but the expansion of metal rods heated [1]. However the extremely tiny coefficient of
thermal expansion of metal or alloy obliged us to look for a good approach to amplify the micro
displacements, then a concise way to get big displacement was designed [2].
It is well known, that both magnetostrictive and giant magnetostrictive materials change their
sizes and shapes when they are placed in a magnetic field, and such an effect is called a
magnetostrctive effect. Similarly, a converse piezoelectric and electrostrictive effect occurs when
some crystals are positioned in an electric field; likewise, the generation of strain induced by the
irradiation of light is defined as a photostrictive effect.
All above effects produce, to a different extent, microdisplacements (expansion or contraction),
which are vertical or parallel to external fields (a magnetic or electric or irradiation light field).
There is a great deal of applications based on the principle that strains occur when external fields
are applied on some materials. The applications relate to the aerospace or the defense industry,
electronics, machinery, petroleum, textile, agricultural and other fields [3- 6].
For the material of magnetostrictive effect, the magnetostrictive coefficient is essential among
several parameters (magnetostrictive coefficient, mechanical energy to electrical energy
conversion arte, energy density, response speed, reliability, driving mode, working frequency

2. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
2
range and stability, etc.) to characterize the magnetostrictive material (such as CoFe2O4) and giant
magnetostrictive material (such as TbFe2, SmFe2 (with magnetostrictive coefficient 1.753×10-3
,-
1.560×10-3
,respectively). Generally speaking, the larger the magnetostrictive coefficient ݀௜௝, the
more useful the magnetostrictive material is. The relationship of strain ߝ௜, ݀௜௝ and the external
magnetic field ‫ܪ‬௜can be depicted by the equation (1) below
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬
ߝଵ
ߝଶ
ߝଷ
ߝସ
ߝହ
ߝ଺‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
=
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬
݀ଵଵ݀ଶଵ݀ଷଵ
݀ଵଶ݀ଶଶ݀ଷଶ
݀ଵଷ݀ଶଷ݀ଷଷ
݀ଵସ݀ଶସ݀ଷସ
݀ଵହ݀ଶହ݀ଷହ
݀ଵ଺݀ଶ଺݀ଷ଺‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
൥
‫ܪ‬ଵ
‫ܪ‬ଶ
‫ܪ‬ଷ
൩---------------------------------------------------- (1)
For the converse piezoelectrictive and electrostrictive effects can be depicted by equation (2),
where ߝ௜, ݀௜௝,, ‫ݏ‬௜௝ and ‫ܧ‬௝ presents strain, converse piezoelectristive coefficient, photostrictive
coefficient and electric intensity, respectively.
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬
ߝଵ
ߝଶ
ߝଷ
ߝସ
ߝହ
ߝ଺‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
=
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬
݀ଵଵ݀ଶଵ݀ଷଵ
݀ଶଵ݀ଶଶ݀ଶଷ
݀ଷଵ݀ଷଶ݀ଷଷ
݀ସଵ݀ସଶ݀ସଷ
݀ହଵ݀ହଶ݀ହଷ
݀଺ଵ݀଺ଶ݀଺ଷ‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
൥
‫ܧ‬ଵ
‫ܧ‬ଶ
‫ܧ‬ଷ
൩ +
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬
‫ݏ‬ଵଵ‫ݏ‬ଵଶ‫ݏ‬ଵଷ
‫ݏ‬ଶଵ‫ݏ‬ଶଶ‫ݏ‬ଶଷ
‫ݏ‬ଷଵ‫ݏ‬ଷଶ‫ݏ‬ଷଷ
‫ݏ‬ସଵ‫ݏ‬ସଶ‫ݏ‬ସଷ
‫ݏ‬ହଵ‫ݏ‬ହଶ‫ݏ‬ହଷ
‫ݏ‬଺ଵ‫ݏ‬଺ଶ‫ݏ‬଺ଷ‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
቎
‫ܧ‬ଵ
ଶ
‫ܧ‬ଶ
ଶ
‫ܧ‬ଷ
ଶ
቏-------------------------- (2)
Both the converse piezoelectric and electrostrictive materials (such as BaTiO3 and
Pb(‫݃ܯ‬భ
య
ܾܰమ
య
)O3, respectively) can be transverse or longitudinal.
Researchers have been laboriously looking for the materials with larger magnetostrictive
coefficients. The giant magnetostrictive coefficients, such as TbFe2 and SmFe2 with 1.753× 10-3
and -1.560 × 10-3
respectively, are much larger than that of conventional magnetostrictive
materials. Even so, its magnitude is still not big enough, in the order of magnitude of 10-3
.
Therefore, the amplification of the micro-displacement is very significant for practical
applications. This simple method reported here increases the displacement dozens, and even more
than one hundred times, with ease. Comparing all previous ways to amplify micro displacement
[7-9], although this system consists of only some mechanical rods, no relative sliding motion
occurs, so that not any phase delay yields at all when the external magnetic field is alternating.
Therefore, it can satisfy the amplification of displacements caused by a high frequency magnetic
field. It is obvious that two displacements created by two rods of materials can be added directly.
It is easy to imagine, in principle, there is no limitation to this amplification.
In order to obtain larger displacement, we generalized the basic idea proposed in the thermal
expansion case. We first describehow to enlarge displacement produced by the magnetostrictive
effect in detail, and then extend the design to converse piezoelectric effect, photostrictive effect
cases briefly.

3. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
3
2. THE DESIGNS OF THE AMPLIFICATION
The principle of amplification of micro displacement is shown in Fig.1. The main components are
two kinds of rigid rods (1) and (2) made from magnetostrictive (or giant magnetostrictive)
materials, with positive ݀ଷଷ and negative ݀ଷଷ (see Fig.2) connected by non-magnetostrictive rods
(3) rigidly. Two magnetostrictive rods will get longer and shorter, respectively, when magnetic
fields are exerted on the amplified system. The direction of the magnetic field should be decided
by the properties of material rods, transverse or longitudinal magnetostriction. For the transverse
magnetostrictive material, the orientation of the external field is perpendicular to the direction of
the magnetic field, and for longitudinal one along the direction of magnetic field.
3. A CONCRETE EXAMPLE
One concrete example is given as following:TbFe2 giant magnetostrivtive alloy [10,11]with the
positive magnetostrictive coefficient +1.753× 10-3
, was selected as the red material rods (1)
(shown in Fig. 1) and SmFe2 with -1.560× 10-3
the green rods (2) in the same figure [12].Let ݈be
red and green long rod, with100 cm in length, cut both rods into 5 segments with 20 cm long. The
net total displacements for the system, in external saturation magnetic field,can be calculated by
the equation below:
∆݈ = ൣሺ5 + 1ሻ݀ଷଷ,்௕ி௘మ
+ 5|݀ଷଷ,ௌ௠ி௘మ|൧݈
= ሾ6 × 1.753 × 10ିଷ
+ 5|−1.560 × 10ିଷ|ሿ × 200 ݉݉ = 3.66 ݉݉
3.66 mm is a macro-size that can be seen by naked eye. The size of whole device is reduced from
100 cm into 20 cm, and what’s more, the current to create the saturation magnetic field can be
decreased considerably.
Of course, besides|݀ଷଷ,ௌ௠ி௘మ
|, some others dij components also are not equal to zero. Fortunately,
the rods can be placed symmetrically based on the concrete values ofdij, so that the distortion
displacements can be cancelled each other completely.
4. SOME SIMILAR DEVICE FOR AMPLICATION
Similarly, the red rod (1) (as shown in Fig. 3) with positive converse piezoelectric (or
electrostrictive) coefficient ݀ଷଷ will get longer along the vertical direction, while the green rod (2)
will get shorter when the external electric field is exerted. The working principles of two
electrodes (4) and (5) depend on whether the red and green rods are longitudinal or transverse.
One can coordinate the relationship among positive or negative strain coefficients, longitudinal
(or transverse)piezoelectric (or electrostrictive) effect, to obtain additional net displacements
caused by red and green rods.
Finally, by irradiating asymmetric piezoelectric ferroelectrics (such as PLZT), with light, an
electric field is caused by the photovoltaic effect. The electric field then causes a mechanical
strain by the piezoelectric effect. The amplification of microdisplacement caused by the
photostrictive effect is shown in Fig. 4. The red (or green) rods stand for photostrictive material
with positive (or negative) transverse photostrictive coefficients݀ଷଷ. Thetotal displacement equals
the summation of the positive and the absolute value of the negative displacement. As the number
of strain rods increase, the amount of displacements increases linearly. This effect can be applied

4. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
4
to a specific bender. When the light irradiates on some photostrictive material rods which are
attached to a piece of non-photostrictive plate, the bender begins to bend. When its
microdisplacement is amplified by this method, the displacement amount will increase many
times more than the amount by the normal way.
5. SUMMARIES AND CONCLUSIONS
In contrast with all other methods, up to now, to amplify microdisplacements, this simple one
holds some unique advantages that can suitable to the external fields with high frequency because
the joint of the rods are all rigid. Conversely, the traditional approaches, all are based on the
principle of lever, consequently, the existence of friction forces between materials rods will delay
the response to the external fields. It is obvious lots of times of amplification of
microdisplacement can be gained with ease by assembling all kinds of material to respond to
different external fields.
Figure.1 The illustraction of the principle to amplify a microdisplacement caused by
magnetostrictive effect
(1) Material rod with positive magnetostrictive (or giant-magnetostrictive) coefficient;
(2) material rod with negative magnetostrictive (or giant-magnetosrictive) coefficient;
(3) non-magnetostrictive material rod to connect 1 and 2;
(4) magnet to create vertical magnetic field;
(5) magnet to create horizontal magnetic field.

5. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
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Figure.2 Dependence of the longitudinal magnetosctriction of a number of polycrystalline metals,
alloys and compounds on magnetic field intensity
Figure. 3 The illustraction of the principle to amplify a micro-displacement caused by
converse piezoelectric or electrostrictive effect
(1) material rod with a big and positive converse piezoelectric or electrostrictive
coefficient;
(2) material rod with big and negative converse piezoelectric or electrostrictive
coefficient;
(3) non-converse or electrostictive rod to connect (1) and (2);
(4) electrodes to create horizontal electric field;
(5) electrodes to create vertical electric field.

6. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
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Figure. 4 The illustractin of the principle to amplify the micro-displacement caused by
photosctrictive effect
(1) material rod with positive photostrictive coefficient;
(2)material rod with negative photostrictive coefficient or non-photostrictive material;
(3) non-photostrictive material to connect 1 and 2;
(4) incident light
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7. International Journal of Instrumentation and Control Systems (IJICS) Vol.6, No.2/3, July 2016
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[8] Pengchen Xie, Weiming Yang and Yuming ding, Chinainvention patent authorization number:
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